Post #17

Last week in calculus was review week. We didn't learn anything new so I'm going to review some of the old stuff because it will be on our exam.

Tangent Line:

1. If you are only given a x value, plug into your equation to find the y value.

2. take the derivative of the equation

3. Plug in your x value into the derivative to find the slope

4. Put in point slope

EXAMPLE: y=3x^3 + 4x^2 +5 at x=1

1. 3(1)^3+4(1)^2+5 = 12

2. 9x^2 + 8x

3. 9(1)^2 + 8(1) = 17

4. y-12 = 17 (x-1)

Normal line is the same except you take the negative reciprocal of the slope to plug in.

y-12 = -1/17 (x-1)

Rolle's Theorem:

In order to use Rolle's theorem, the fuction must be continuous and differentiable on the interval given and f(a) = f(b)

Example:

-x^2+14x on [0,14]

The function is continuous and differentiable

f(0) = -(0)^2 + 14(0) = 0

f(14) = -(14)^2 + 14(14) = 0

Therefore Rolle's applies

Now take the derivative: -2x+14

and set equal to zero: -2x+14 = 0

solve for x: x=7 or c=7

Mean value theorem:

The function again has to be continuous and differentiable at the interval given and you plug into f(b) - f(a) / b-a

Example: x^2 on [1,7]

The function is continuous and differentiable

First take the derivative: 2x

Then plug into the formula: f(7) - f(1) / 7-1

14-2/ 7-1 = 12/6 which equals 2.

I am still having troubles with graphs and going from one graph to another. I don't understand how to find increasing/decreasing, concave up/down, maxs, mins, and points of inflection. Help please!